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Learning the dynamics of a physical system wherein an autonomous agentoperates is an important task. Often these systems present apparent geometricstructures. For instance, the trajectories of a robotic manipulator can bebroken down into a collection of its transitional and rotational motions, fullycharacterized by the corresponding Lie groups and Lie algebras. In this work,we take advantage of these structures to build effective dynamical models thatare amenable to sample-based learning. We hypothesize that learning thedynamics on a Lie algebra vector space is more effective than learning a directstate transition model. To verify this hypothesis, we introduce the GroupEnhanced Model (GEM). GEMs significantly outperform conventional transitionmodels on tasks of long-term prediction, planning, and model-basedreinforcement learning across a diverse suite of standard continuous-controlenvironments, including Walker, Hopper, Reacher, Half-Cheetah, InvertedPendulums, Ant, and Humanoid. Furthermore, plugging GEM into existing state ofthe art systems enhances their performance, which we demonstrate on the PETSsystem. This work sheds light on a connection between learning of dynamics andLie group properties, which opens doors for new research directions andpractical applications along this direction. Our code is publicly available at:https://tinyurl.com/GEMMBRL.

GEM: Group Enhanced Model for Learning Dynamical Control Systems